A particle moves along a curve of unknown shape but magnitude of force `F` is constant and always acts along tangent to the curve.Then

Options

A. F many be conservative
B. F must be conservative
C. F may be no-conservative
D. F must be non-conservative

Answer

To solve the problem, we need to analyze the motion of a particle moving along a curve under the influence of a constant force that always acts tangentially to the curve.

### Step-by-Step Solution:

1. **Understanding the Force**:
- The problem states that a particle moves along a curve and the force \( F \) is constant in magnitude and always acts along the tangent to the curve at any point.

2. **Work Done by the Force**:
- The work done \( W \) by a force is given by the integral of the force along the path of motion. Since the force is always tangential to the curve, the work done can be expressed as:
\[ W = \int F \cdot ds \]
- Here, \( ds \) is the differential displacement along the curve.

3. **Calculating Work Done**:
- Since the force \( F \) is constant in magnitude and always acts along the tangent, we can simplify the expression for work done:
\[ W = F \int ds = F \cdot L \]
- Where \( L \) is the total length of the path traveled by the particle.

4. **Nature of the Force**:
- A conservative force is defined as one where the work done does not depend on the path taken, but only on the initial and final positions. In this case, since the work done depends on the path length \( L \), it indicates that the force is non-conservative.

5. **Conclusion**:
- Therefore, we conclude that the force acting on the particle is a non-conservative force.

### Final Answer:
The correct option is **D** (the force is non-conservative).